王本锋, 吴如山, 陈小宏, 陆文凯

1 清华大学自动化系，智能技术与系统国家重点实验室, 北京　100084　2 中国石油大学(北京)油气资源与探测国家重点实验室， 北京　102249　3 Modeling and Imaging Laboratory, University of California, Santa Cruz，95064, U.S.A.



基于T-matrix的非线性参数估计方法

王本锋1,2,3, 吴如山3, 陈小宏2, 陆文凯1

1 清华大学自动化系，智能技术与系统国家重点实验室, 北京1000842 中国石油大学(北京)油气资源与探测国家重点实验室， 北京1022493 Modeling and Imaging Laboratory, University of California, Santa Cruz，95064, U.S.A.

摘要全波形反演可提供高精度的地下介质参数空间分布，但传统的全波形反演方法建立在Born近似的基础上，对初始模型具有一定的依赖性.为了摆脱Born近似的束缚，本文基于二维常密度声波方程，在De Wolf近似的前提下，借助传输矩阵(T-matrix)方法，深入研究了逆薄板传播算子(Inverse Thin-Slab Propagator, ITSP)，实现了速度扰动的非线性估计.ITSP方法避免了Born级数方法在扰动较强、扰动区域较大时的发散性问题，且只经过一次扫描校正，计算效率较高.二维模拟数据分析验证了本文方法的可行性以及有效性.

关键词全波形反演； De Wolf 近似； 传输矩阵； 逆薄板传播算子； Born级数

The Inverse Thin-Slab Propagator (ITSP) is studied in detail both theoretically and numerically based on Transmission Matrix (T-matrix) and De Wolf approximation using the 2D acoustic wave equation with constant density, which can overcome the limitations of Born approximation. The ITSP method considers all orders of scattering effects and has no initial model dependence, besides, it is a regularized method in each correction step and has no divergence effects. One correction sweep (half from upper part, half from lower part) is involved and is computationally efficient. Based on the ITSP method, the velocity perturbation can be achieved and the velocity distribution can be obtained finally with the background velocity.

We designed three numerical models including ellipse ball with positive velocity perturbations, Gaussian ball with negative velocity perturbations and ellipse ball with both positive and negative velocity perturbations. With the ITSP method, we achieve the velocity distribution based on the known T-matrix and the T-matrix estimation method will be left for future research. The reconstructed results are consistent with the true velocity distributions and the relative errors are minor enough for these three models, which demonstrate the validity of the proposed method. Using the ITSP method, only one correction sweep is involved to achieve the velocity distribution, and it is time efficient. Therefore, this nonlinear estimation method may have wide applications in the future.

The accurate velocity distribution is achieved based on the known T-matrix using the ITSP method. 2D numerical examples of the designed models including different perturbation types, demonstrate the validity of the proposed method. The ITSP method considers all scattering effects and overcomes the initial model dependence of Born approximation, besides, it is a regularized method in each correction step and overcomes the divergence effect of Born series for strong velocity perturbation or large perturbation volume. It is also time efficient because only one correction sweep is involved (half from upper part, half from lower part). This method is based on the known T-matrix, suitable for smooth media, then T-matrix estimation method and the improved ITSP method for complex media will be developed in future work.

1引言

随着勘探开发的不断深入，地震勘探逐渐进入岩性油气藏勘探阶段，对地震资料处理以及反演提出了更高的要求.全波形反演可以精确描述地下介质参数空间分布，但是其巨大的计算量以及对初始模型的依赖性，成为其广泛应用的瓶颈(Virieux and Operto, 2009).为了克服其计算量大的缺陷，GPU加速技术、相位编码技术以及震源编码技术被相继利用，达到提高计算效率的目的(Ben-Hadj-Ali et al., 2009; Larner et al., 1981; Luo et al., 2012; Moghaddam et al., 2013).由于计算量大的限制，大多数反……